Answer: June 30th
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Explanation:
Here's a table to show the dates for each visit:
[tex]\begin{array}{|c|c|c|} \cline{1-3}\text{Number} & \text{Library} & \text{Veterinarian}\\\cline{1-3}1 & \text{June } 6 & \text{June } 10\\\cline{1-3}2 & \text{June } 12 & \text{June } 20\\\cline{1-3}3 & \text{June } 18 & \textbf{June 30}\\\cline{1-3}4 & \text{June } 24 & \text{July } 10\\\cline{1-3}5 & \textbf{June 30} & \text{July } 20\\\cline{1-3}\end{array}[/tex]
The only thing in common between both columns is "June 30". This happens on the library's 5th visit and the veterinarian's 3rd visit.
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Effectively we're listing out the multiples of 6 and 10 like so
multiples of 6 are: 6, 12, 18, 30, 36, 42, ...
multiples of 10 are: 10, 20, 30, 40, 50, ...
We can see the LCM is 30, which directly leads to "June 30".
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An alternative approach is to find the GCF of 6 and 10. That would be 2.
Then we can say this:
LCM = (6*10)/GCF = 60/2 = 30
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Another way to find the LCM
6 = 2*3
10 = 2*5
The unique factors are 2, 3, 5 which multiply to 30.
